Question #43351

A potentiometer wire of initial length $L_0 = 100\text{ cm}$ and resistance $R_{w0} = 100\ \Omega$ is rigidly clamped at both ends so that its length cannot change. It is connected in series with a resistance $R_s = 105\ \Omega$ and a primary cell of EMF $E_0 = 10\text{ V}$ (with negligible internal resistance). A secondary cell of EMF $E_1 = 2\text{ V}$ is balanced on this wire. The temperature of the potentiometer wire is then uniformly increased by $\Delta T = 50^\circ\text{C}$. Given the following properties for the wire material: temperature coefficient of resistivity $\gamma = 1.6 \times 10^{-3}\ ^\circ\text{C}^{-1}$, coefficient of linear thermal expansion $\alpha = 2.0 \times 10^{-4}\ ^\circ\text{C}^{-1}$, and Poisson's ratio $\nu = 0.5$. Assuming the clamps and the series resistor $R_s$ do not change temperature, what is the magnitude of the shift in the null point?